# Differentiation Problem

• Mar 2nd 2009, 08:15 PM
soldatik21
Differentiation Problem
Can anyone help me out with this one problem please, didn't really learn this type of problem yet.

find a and b such that f is differentiable everywhere

f(x)= ax^3, x=less than or equal to 2
x^2+b, x=greater than 2

thanks
• Mar 2nd 2009, 08:17 PM
Prove It
Quote:

Originally Posted by soldatik21
Can anyone help me out with this one problem please, didn't really learn this type of problem yet.

find a and b such that f is differentiable everywhere

f(x)= ax^3, x=less than or equal to 2
x^2+b, x=greater than 2

thanks

Hint: If $f(x)$ is differentiable everywhere, then it is continuous and smooth at all points.

Here, the only possible point of discontinuity is at $x = 2$.

So you need to find an $a$ and $b$ so that the function is the same at that point.

Have a go.
• Mar 2nd 2009, 08:25 PM
soldatik21
i understand that part that at x=2 the two functions have to be equal. but doesn't that give you more than one answer for example a can be 2 and can be 12? or a can be 1 and b can be 4?